The Bronx Zoo is many times larger and more elaborate than the Central Park Zoo, and has the adjacent botanical gardens. That said, it is a bit of a journey from Manhattan, where I presume you'll be staying. It would take up most of a day to see and return from. And I doubt that it's that different from the major zoos in the UK or Europe. My recommendation, unless you are huge zoo fans, would be to do a much quicker visit to the Central Park Zoo and use the time left to see something else.
Here's something that my DC had great fun visiting:
https://intrepidmuseum.org/
It's the Intrepid Sea, Air and Space Museum. You get to tour a decommissioned aircraft carrier and submarine, and see a retired space shuttle up close. And it's very easy to get to.
Another lesser-known attraction is the Radio City Music Hall Stagedoor tour:
https://www.msg.com/guided-tours/new-york-city-tours/radio-city-music-hall-tour
A Rockette (member of the dance troop) takes you backstage in this famous Art Deco theater. You get to see the props, costume rooms, backstage mechanical, and vintage artifacts. It takes only an hour and is centrally located in Rockefeller Center.
It's too late to book dinner, but you might be able to book lunch here:
https://www.unionsquarecafe.com./
The food and decor are fabulous, as is the service. It's the flagship restaurant in a group owned by one of NY's best restaurateurs. It's also on the casual side, with good choices for the kids. It's my all-around favorite place to eat in NYC.